Problem 2 [50'] Consider the following intentor}r problem. A camera store stocks a particular model camera that can he ordered weekly. Let ,1 he the demand of the camera in the n-th Mk. Amume {Dnil are independent and identically distributed random variables and have the following prohahilitg,r mass function EE-Il- Let X" he the inventory level at the end of week 11. Suppose XE = 3. The ordering policyr is as follows. If X" 5 1, then order up to .3. For example. if X\" =11 meaning there are only 1 items in the store at the end of week 11.. then order 2 items over the weekend so that next .Monday morning there are 3 items in the store [i.e. there are 3 items in the beginning of week :1 + 1}. If X\" 2 2. do not order. {a} It can he shown that {In '. n 3_'-' D} is a discrete time Markov chain. Please write down the transition matrix. {h} Suppose the storage cost for holding the camera on hand is C(] = U.C{1] = 21 C(12) = E. C(11) = 12. Then what is the long-run expected average cost per unit time for the store